Question

The heart is pumping blood at x kg per unit time, with constant velocity $v$. The force needed is:

• A. $xv$
• B. $v\frac{dx}{dt}$
• C. $x\frac{dv}{dt}$
• D. $zero$

Answer 1

Answer: (A)

$xv$

Force is defined as the rate of change in momentum.

$F=\frac{dP}{dt}$ (where $P$ is momentum)

$P=mv=$ mass $\times$ velocity

$F=\frac{dP}{dt}=\frac{d\left(mv\right)}{dt}=\frac{dm}{dt}v$ ; When velocity is constant and mass flow is changing

Here it is given that mass flow rate is $xkg$

So, $\frac{dm}{dt}=x$

$F=\frac{dm}{dt}v=xv$